Happiness is a factor that influences several things in the game. There are three states of happiness that can exist:
|75% or less||Citizens are Happy!|
Build more houses to increase your population.
Citizens are Unhappy
|90% or greater||
Citizens are Very Sad
A higher happiness level means businesses will be collected from faster.
It is probable that there is a higher % chance of collecting bonus population when getting rent for happy as opposed to unhappy.
It is unknown what the actual chances of getting the bonus population are, and if they are the same for all residences. If so, residences that are collected more frequently (faster recharge times) would be able to get the bonus population faster as opposed to those that take days.